Swept signal analysis instrument and method

ABSTRACT

The sweep rate limitations that heretofore have constrained the maximum sweep rates of swept analysis instruments are obviated by optimizing filter circuitry and post-processing the IF signal using various techniques to compensate for errors caused by fast sweeping.

FIELD OF THE INVENTION

The present invention relates to swept signal analysis instruments, suchas spectrum analyzers and network analyzers, and more particularlyrelates to a method and apparatus permitting such instruments to beswept at fast rates.

BACKGROUND AND SUMMARY OF THE INVENTION

The term "swept signal analysis instrument" as used herein is a genericterm referring to any electronic equipment in which an input signal ismixed to an intermediate frequency using a swept local oscillator and issubsequently filtered.

The most common swept signal analysis instruments are spectrum analyzersand network analyzers, and it is with reference to these instrumentsthat the present invention is illustrated. In a spectrum analyzer, aninput signal to be analyzed is heterodyned to an intermediate frequency(IF) using a swept local oscillator. The IF signal is filtered with anarrow bandwidth IF filter. The swept local oscillator has the effect of"sweeping" all the frequencies of the heterodyned-down input signal pastthe fixed frequency of the IF filter, thereby permitting the filter toresolve the input signal's spectral composition. The signal power withinthe filter bandwidth is determined by a detector cascaded after the IFfilter and is typically displayed on a graphical display associated withthe instrument.

A network analyzer is similar in many respects to a spectrum analyzerbut instead of analyzing an unknown signal, the instrument analyzes anunknown network. To do this, the instrument excites the unknown networkwith a known signal and monitors the phase and amplitude characteristicsof a resultant signal, thereby permitting the network's transferfunction to be characterized. Again, the instrument relies on a sweptlocal oscillator to heterodyne the input signal to an intermediatefrequency, and the IF signal is again filtered prior to analysis. In anetwork analyzer, however, the IF filter serves to eliminate noiseeffects rather than to provide a narrow resolution bandwidth, and thefiltered IF signal is analyzed to determine the phase and amplitude ofthe IF signal rather than its power. The analysis further includes"normalizing" the IF signal to the original excitation signal in orderto reduce excitation source related errors.

All swept signal analysis instruments suffer from a common limitation,namely measurement errors caused by the sweeping operation. In spectrumanalyzers, these errors manifest themselves as a degradation in theperformance of the IF filter. As the sweep speed increases, spectralcomponents of the input signal are swept at increased speeds through thefilter. The behavior of the filter to these quasi-transient signals canbe optimized by using a Gaussian filter response, thereby minimizingconventional dynamic problems such as ringing and overshoot. However,above a certain sweep rate, even an ideal Gaussian filter becomesunsatisfactory due to spreading of the filter passband and errors inamplitude (i.e. power) response. In particular, the filter passbandapproaches its impulse response shape when the sweep rate increases toinfinity, and the amplitude of the response decreases with the squareroot of the sweep rate.

An ideal Gaussian response is often approximated by cascading aplurality of single-tuned filter stages. (A true Gaussian responsecannot be physically realized since it is noncausal.) These cascadedstages generally include capacitors, inductors or crystals, and thushave transfer functions with poles. All transfer functions with polesexhibit non-flat group delay, also known as nonlinear phase response.One problem with such filters is that they respond more quickly to theleading edge of an input transient signal than the trailing edge.Another problem is that the trailing edge often exhibits notches andringing rather than a smooth fall to the noise floor. Small signals aredifficult to differentiate from aberrations on the falling edge ofnearby larger signals.

These problems, in conjunction with the magnitude errors caused by fastsweeping, have limited traditional analyzers to a maximum sweep rate ofone half the filter bandwidth squared (0.5 BW²). At this rate, themagnitude error is about 1.18%, or less than 0.1 dB--generallyconsidered to be an acceptable accuracy.

The mathematical derivation of the amplitude error and of the passbanddistortion resulting from fast sweeping is set forth in Hewlett-PackardApplication Note 63, May 1965 An article by Tsakiris entitled"Resolution of a Spectrum Analyzer Under Dynamic Operating Conditions,"Rev. Sci. Instrum., Vol. 48, No. 11, November, 1977 contains a similaranalysis for a variety of spectrum analyzer filters.

In network analyzers, sweep related errors manifest themselves as errorsin normalization and as irregularities in both the frequency and phaseresponse of the noise limiting filter. Again, these errors increase withsweep speed and limit the maximum rate at which a network analyzer cansweep through a frequency range of interest.

In accordance with the present invention, the sweep rate limitationsthat heretofore have constrained the maximum sweep rates of sweptanalysis instruments are obviated by optimizing the filter circuitry andpost-processing the IF signal using various techniques to compensate forfast sweeping errors.

The foregoing and additional features and advantages of the presentinvention will be more readily apparent from the following detaileddescription thereof, which proceeds with reference to the accompanyingdrawings.

BRIEF DESCRIPTIONS OF THE DRAWINGS

FIG. 1 is a plot showing several bandwidths of Gaussian filter overseveral decades of sweep rate.

FIG. 2 is a schematic block diagram of a spectrum analyzer according toone embodiment of the present invention.

FIG. 3 is a schematic block diagram of a digital IF filter used in thespectrum analyzer of FIG. 2.

FIG. 4 is a schematic diagram of an IF filter comprised of a pluralityof cascaded synchronously tuned filter stages.

FIG. 5 is a partial schematic block diagram of a network analyzeremploying a 3 tap FIR digital filter to correct for a parabolic phasesweeping error.

DETAILED DESCRIPTION

Analysis of the response of an ideal Gaussian filter to swept frequencyinput signals shows that the response is both perfectly predictable andthat none of the distortion apparent in traditional implementationsexists.

Improved filters, with close to Gaussian magnitude response and flatgroup delay, may be "overswept." The amplitude of stationary signalsdecreases in a predictable manner that is a function of the bandwidthand the sweep rate, and that amplitude change may be used ascompensation to provide accurate amplitude measurements.

Analysis also shows that, for a fixed sweep rate, a narrower thantraditional bandwidth actually provides an improved signal to noiseratio. The signal to noise ratio is maximized when the sweep rate andresolution (filter) bandwidth are related by the following equation:

    Sweep rate=2.266(BW.sup.2)                                 (1)

In this event, the signal to noise ratio is almost 2 dB better than attraditional bandwidths. This is due to the fact that the signal leveldecreases only about 1 dB because of the "oversweeping," while the noiselevel decreases about 3 dB.

FIG. 1 shows several bandwidths of Gaussian filter over several decadesof sweep rate. The effect of different sweep rates and bandwidths onsignal to noise ratio can readily be seen.

A further aspect of swept spectrum analysis that is improved by thisinvention is frequency resolution of signals. Improved resolution meansbeing able to differentiate siqnals that are closer together. A usefulconcept to introduce is that of "apparent resolution." This is definedas the bandwidth of the swept response at some appropriate level belowthe peak response.

It is generally known that the response of a filter to a swept signalapproaches the steady state frequency response when swept slowly, andthe filter's response approaches its impulse response when swept veryquickly. An ideal Gaussian frequency response filter has a Gaussianimpulse response. The apparent resolution of a Gaussian filter isexactly its resolution bandwidth when swept slowly. As a Gaussian filteris swept more quickly, the apparent resolution gets wider, but theresponse remains Gaussian. Even at traditional sweep rates, the apparentresolution is a few percent wider than the nominal resolution bandwidth.

Further analysis shows that, for a fixed sweep rate, the apparentresolution is narrower when the actual bandwidth is less thantraditional. This is due to the fact that, although the apparentresolution of the filter gets wider when overswept, the startingresolution was better. In fact, the optimal filter bandwidth for minimumapparent resolution is the same filter bandwidth that maximizes signalto noise ratio. The apparent resolution gets worse for even smallerbandwidths because the filter response is approaching its impulseresponse. The length of the impulse response varies inversely as thebandwidth.

With the foregoing as background, and referring to FIG. 2, a spectrumanalyzer 10 according to one embodiment of the present inventionincludes an analog input 12, a mixer 14 with an associated swept localoscillator 16, an analog IF chain 18, analog-to-quadrature digitalconversion circuitry 20, and post-processing circuitry 22.

The analog IF chain 18 includes an IF filter 24 that sets the resolutionbandwidth of the analyzer. According to one embodiment of the presentinvention, the behavior of this filter is optimized by improving itsphase response and group delay characteristics.

It will be recognized that filter 24 may take several forms. In oneembodiment, the filter is implemented in analog form, with cascadedlumped elements or crystals, or surface acoustic wave technology. Suchfilters can be equalized to yield magnitude response close to Gaussian,effectively eliminating unacceptable responses that cause distortions inthe detected spectrum. In other embodiments, the filter is implementedin a finite-impulse-response (FIR) design, thereby achieving perfectlyflat group delay. (In this latter embodiment, of course, the IF signalmust be converted into digital form prior to filtering.) Again, nearlyGaussian response can be obtained, thereby greatly reducingfilter-induced distortion mechanisms.

The analog-to-quadrature digital conversion circuitry 20 includes ananalog-to-digital converter circuit 26, a pair of mixers 28, 30, and acorresponding pair of low pass filters 32, 34 (which preferably have alinear phase [flat group delay]characteristic). The analog-to-digitalconverter 26 samples the IF signal at periodic intervals and outputs aseries of digital data samples corresponding thereto. These digitalsamples are multiplied with sinωt and cosωt signals by the mixers 28, 30to yield digital representations of the real and imaginary components ofthe IF signal. Linear-phase (or flat group delay) filters 32, 34 filterthe quadrature signals at baseband, equivalent to providing alinear-phase (or flat group delay) filter centered at the frequencyω_(IF) /2πHz.

Quadrature analog-to-quadrature digital conversion circuitry 20 isgenerally known in the art, as described, inter alia, in U.S. Pat. No.4,594,555, the disclosure of which is incorporated herein by reference.

The filters 32, 34 in the illustrated embodiment are implementeddigitally, as shown in FIG. 3. In the illustrated filter topology, thetap coefficients are selected to be powers of two, thereby permittingthe use of bit shifters instead of multiplier stages. Each filter isimplemented with 24-bit logic and a sample clock rate of 250 KHz toprovide a filter bandwidth of 18 KHz. (Actually, a single filter is usedfor both real and imaginary data by multiplexing data through the filterat twice the sample rate.) Narrower filter widths can be achieved byfiltering the IF signal repeatedly through IF filter 24, effectivelyhalving the data bandwidth and sample rate for each pass through thefilter. (The theory and implementation of such "decimation" filtering isprovided in U.S. Pat. No. 4,881,191, which is also incorporated hereinby reference.) Of course, filters 32, 34 can alternatively beimplemented in analog form, if desired.

Even with the use of a Gaussian filter response, the analyzer will stillexhibit an amplitude decrease of about 0.1 dB when swept at 0.5 BW², andmore at faster rates. This amplitude decrease can be corrected bypredicting the loss and applying a compensating sweep-dependent gain.The gain can be applied any place in the signal path. In mostimplementations, the compensating gain is applied in a CPU controlledpost-processing stage 22 that may include a calibration memory 36.

The required compensation can be predicted in at least three ways. Inthe first, it can be computed using the solution of a swept Gaussianresponse. This approach is attractive because the solution exists inclosed-form equations (as shown in the Tsakiris paper, supra) and isthus computationally efficient. In the second technique, the requiredcompensation can be simulated, such as by using a computer model of theactual filter. This approach is more precise than approximating the truefilter response as Gaussian, but is more computationally intensive.However, simulations can be performed at a number of sweep rates, andthe compensations saved in a table for later use. Compensations forsweep rates other than the ones simulated can be interpolated from thevalues in the table. In the third compensation technique, the requiredcompensation can be actually measured in the spectrum analyzer system.This can be done by sweeping through a known amplitude signal at thedesired rate and measuring the decrease in amplitude. This is attractivebecause it takes variations in each individual instrument into account.Again, interpolation can be used to minimize the number of measurementsthat have to be made.

The fast sweeping also introduces an apparent frequency shift in theresulting data. This frequency shift can also be predicted (either inclosed mathematical form [the formula is given in the Tsakiris paper])or by one of the other techniques noted above. Once predicted, it cansimilarly be compensated for.

It will be recognized that the above-described embodiment providesseveral improvements to the art. One is the use of approximatelygaussian filters of linear phase to a signal analysis instrument. Whilethe amplitude response of such a filter may not be a substantialimprovement over prior art cascaded synchronous single-tuned filterstages, the phase response is. That is, the linear-phase filteringemployed in the illustrative embodiment offers the instrument asymmetric passband with essentially no ringing under dynamic conditions.The Tsakiris article indicates that asymmetric passband and dynamicringing are unavoidable in such instruments.

Another improvement is the improved sensitivity and resolving power thatcan be achieved by "oversweeping" using a smaller than traditionalbandwidth. Again, the Tsakiris article indicates that fast sweeping isto be avoided because it leads to a degradation of resolution andsensitivity.

In a second embodiment of the present invention, the IF filter 24 can beimplemented using a conventional arrangement of a plurality of cascadedsingle tuned filter stages 38, as shown by filter 24' in FIG. 4. In thiscase, the resulting amplitude loss can again be predicted using any ofthe three methods detailed above and can be compensated accordingly.Since the cascaded stages exhibit a non-flat group delay, the filteralso introduces a time delay, which translates into a frequency offset.This error term, too, can be predicted and corrected.

The same basic principles can be used to increase the sweep rate of anetwork analyzer. In this case, the error mechanisms include errors innormalization of the network output signal due to fast sweeping, and theerrors caused by sweeping through the parabolic phase characteristic ofthe instrument's IF (aka noise limiting) filter. These error mechanismscan be determined and compensated.

FIG. 5 shows a network analyzer 38 used to analyze a network under test40. The analyzer 38 includes a swept mixer 42, an IF filter 44, and asimple 3-tap FIR filter 46 cascaded after IF filter 44 to mitigate theeffects of parabolic phase errors. The coefficients (symmetrical) forthe filter 46 are given by the following formulas:

    b.sub.1 =j/4αT.sup.2                                 (2)

    b.sub.0 =1-(j/2αT.sup.2)                             (3)

More complex filter topologies (i.e. more taps) can be used to yieldcommensurately better error compensation.

Another technique of compensating for the parabolic phase error is toadd the results an increasingfrequency sweep to the conjugate of acorresponding decreasing-frequency sweep.

Yet another technique to equalize the parabolic phase error is toperform a Fourier transform on the raw data, multiply by a parabolicphase term, and then perform an inverse Fourier transform.

A final technique to compensate the parabolic phase error is by use of aparallel filter equalizer.

It will be recognized that the analyzer filter 44 windows the frequencytransform of the network under test. The shape of this windowingfunction can be selected to optimize fast sweep speed performance.

If, at the desired sweep rate, the impulse response of the network undertest falls entirely within the filter, then the filter should be flat togive a uniform window.

If, on the other hand, significant energy falls outside of the filter,then an exponential window will be found advantageous.

A variety of other windowing functions are advantageous for differentcircumstances. Accordingly, it is desirable to provide the instrumentwith a plurality of windowing functions and means for selectingtherebetween. The preferred implementation is to provide a single filterand to implement the different windowing functions digitally. (Windowselection is known in digital signal analyzers, but has not heretoforebeen employed in network analyzers.) In such an embodiment, a desirablefilter is the Nyquist zero symbol interference filter.

It will be recognized that all the foregoing error compensationtechniques are independent of the network under test.

Having described and illustrated the principles of our invention withreference to preferred embodiments thereof, it will be apparent thatinvention can be modified in arrangement and detail without departingfrom such principles. For example, while the spectrum analyzer isillustrated with reference to a digital IF filter, it will be recognizedthat a variety of other filters may alternatively be used. For example,surface acoustic wave (SAW) filters can be used and can be made to havenearly flat group delay characteristics. In view of the many possibleembodiments to which the principles of our invention may be put, itshould be recognized that the detailed embodiments are illustrative onlyand should not be taken as limiting the scope of our invention. Rather,we claim as my invention all such embodiments as may come within thescope and spirit of the following claims and equivalents thereto.

We claim:
 1. In a method of spectral analysis comprising thesteps:sweeping a variable frequency oscillator to mix an input signal toan intermediate frequency signal; filtering the intermediate frequencysignal with a filter having a bandwidth BW for resolving a subband offrequencies; and detecting the spectral power of the intermediatefrequency signal within the filtered subband of frequencies to therebydetermine data representing the power of the input signal as a functionof frequency; an improvement wherein; the sweeping step comprisessweeping at a rate faster than 0.5 BW² ; and in which the method furtherincludes compensating for errors introduced into said data by the fastsweeping.
 2. The method of claim 1 in which the compensating stepincludes compensating for frequency shift errors introduced by the fastsweeping.
 3. The method of claim 1 in which the compensating stepincludes compensating for detected power errors introduced by the fastsweeping.
 4. The method of claim 1 in which the filtering step includesapproximating a Gaussian filtering response by filtering theintermediate frequency signal through a plurality of cascaded filterstages with non-flat group delay.
 5. In a method of spectral analysiscomprising the steps:sweeping a variable frequency oscillator to mix aninput signal to an intermediate frequency signal; filtering theintermediate frequency signal to resolve a subband of frequencies havinga bandwidth BW therefrom; and detecting the spectral power of thefiltered subband of frequencies to thereby determine the power of theinput signal as a function of frequency; an improvement wherein: thefiltering step includes filtering with a substantially Gaussian responseand substantially flat group delay; and the sweeping step comprisessweeping at a rate faster than 0.5 BW².
 6. The method of claim 5 inwhich the sweeping step comprises sweeping at a rate of approximately2.266 BW².
 7. The method of claim 5 in which the filtering step includesfiltering with a filter having non-flat group delay and phasecompensating said filtering to provide filtering with a substantiallyflat group delay.
 8. The method of claim 5 in which the filtering stepincludes filtering with a finite-impulse-response filter.
 9. The methodof claim 5 in which the filtering step includes filtering with a surfaceacoustic wave filter.
 10. The method of claim 5 which further includescompensating for errors in the detected power introduced by said fastsweeping.
 11. The method of claim 10 in which the compensating stepincludes computing, using closed-form mathematical equations, thefiltering losses associated with an ideal Gaussian filter at a givensweep rate and compensating therefor.
 12. The method of claim 10 inwhich the compensating step includes simulating actual filtering lossesand compensating therefor.
 13. The method of claim 12 which furtherincludes:simulating actual filtering losses at a plurality of discretesweep rates; storing data corresponding thereto; and interpolating fromsaid stored data to estimate filtering losses at a given sweep rate. 14.The method of claim 10 in which the compensating step includes measuringactual filtering losses and compensating therefor.
 15. The method ofclaim 14 which further includes:measuring the actual filtering losses ata plurality of discrete sweep rates; storing data corresponding thereto;and interpolating from said stored data to estimate filtering losses ata given sweep rate.
 16. The method of claim 5 which further includescompensating for frequency shift errors introduced by said fastsweeping.
 17. The method of claim 1 in which the filtering step includesfiltering with a finite impulse response digital filter.
 18. The methodof claim 17 in which the filtering step includes filtering with a finiteimpulse response digital filter that has symmetrical coefficients toprovide a flat group delay.
 19. The method of claim 8 in which thefiltering step includes filtering with a finite impulse response digitalfilter that has symmetrical coefficients to provide a flat group delay.20. In a method of spectral analysis comprising the steps:sweeping avariable frequency oscillator to mix an input signal to an intermediatefrequency signal; filtering the intermediate frequency signal with afilter having a bandwidth BW for resolving a subband of frequenciestherefrom; and detecting the spectral power of the intermediatefrequency signal within the subband of frequencies to thereby determinedata representing the power of the input signal as a function offrequency; an improvement wherein: the sweeping step comprises sweepingat a rate faster than 0.5 BW² ; and in which the method further includesprocessing said data to compensate for errors introduced by the fastsweeping.
 21. The method of claim 20 in which the processing stepincludes processing said data to compensate for frequency shift errorsintroduced by the fast sweeping.
 22. The method of claim 20 in which theprocessing step includes processing said data to compensate for detectedpower errors introduced by the fast sweeping.
 23. The method of claim 20in which the filtering step includes approximating a Gaussian filteringresponse by filtering the intermediate frequency signal through aplurality of cascaded filter stages with non flat group delay.
 24. Themethod of claim 20 in which the filtering step includes filtering with afinite impulse response digital filter.
 25. The method of claim 24 inwhich filtering step includes filtering with a finite impulse responsedigital filter that has symmetrical coefficients to provide a flat groupdelay.